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{My comments will briefly address Averages (only) in the context of logical fallacy. There is another related discussion that might examine other statistical tools and techniques relating to predictive modeling and forecasting, but we’ll save that for another day & possible question.}
I’m reminded of the old joke that anyone having taken a course in Statistics has probably heard: “My head is in a hot oven and my feet are in a freezer but ON AVERAGE I feel just fine.” This little joke points to a serious potential flaw in taking Averages too monolithically, i.e., drawing conclusions about ‘reality’ from averaging a handful of data points. Most of us accept it as given that if we use or collect “bad data” in e.g., conducting an experiment or compiling a survey, the results will be skewed and any conclusions formed will likely be erroneous. (After all, we’ve been conditioned to accept GI=GO). Far more insidious are the possibilities for reaching a wrong or misleading conclusion (given the data is collected properly) arising from misapplication or misunderstanding of analytical statistical techniques; numerical averaging is one of the most basic. The little joke above points to one glaring problem with averages (there are others): the distribution of the data points, and whether this distribution is normal. If your data points in a survey or experiment fall in a tight cluster, the conclusions drawn from taking a simple average will likely mirror ‘reality’. If the data points are widely & abnormally distributed, a simple average of them (alone) will likely be very misleading. (Plotting out the points using a histogram will help reveal this.) While it is clear that Averaging can be misused and conclusions drawn from so doing can be fallacious, I agree with Bo, this kind of thing is case specific and of itself does not constitute a generic Logical Fallacy. However, there are many references in the literature relating to “The Fallacy of Averages” and some make interesting reading, e.g.: http://derekpilling.com/fallacy-averages/ http://www.seekfind.net/Misuse_of_Averages_Fallacy.html#.WJEGP4L7-6M https://medium.com/@vsglukhov/the-fallacy-of-averages-are-boys-better-in-math-than-girls-dcf3ffad315#.380m7x89i |
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answered on Tuesday, Jan 31, 2017 05:04:54 PM by modelerr |
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